Beyond Distribution Matching: Kinetic Constraints for Unpaired Multi-Omics Alignment

Unpaired static multi-omics data does not clearly answer which cells or molecular states correspond across modalities as distinct multi-omics mappings can produce the same target distribution with potentially biologically impossible states. We introduce Kinetics induced Optimal Transport (KOT), a framework that combines distribution matching with first-order constraints on the differential of the cross-modal mapping itself. KOT pushes an observed source vector field through the mappings own Jacobian, requiring the induced target dynamics to be in agreement with a mechanistic target law, without the need for paired cells or observed target velocities. We show theoretically that this constraint reduces distribution-preserving alignments, that ignore the dynamics of single-cell biology, resulting in identifiability up to shared dynamical symmetries. For RNA–protein transport, biochemical anchors resolve a global kinetic-scale ambiguity. On CITE-seq datasets, KOT reaches competitive performances for cell-level RNA–protein alignment in an unpaired setting. Moreover, a mapping trained only on wild-type cells also transfers to out-of-distribution CRISPR perturbations. Mechanistic ablations show that state correspondence, internal kinetic consistency, and biological dynamics are distinct properties of KOT. Lastly, a chromatin–RNA extension exposes the boundaries of KOT. First-order constraints effect the learned differential, but cannot provide source-field-specific ambiguity resolution when the available chromatin directional field does not contain enough information. These experiments further establish first-order dynamical consistency as an inductive bias for learning unpaired cross-modal correspondences beyond static distribution matching. Code is provided in https://anonymous.4open.science/r/KOT/README.md